I finally found an answer: since commit 85eb73ce there is a pin subcommand available. So ignoring a formula on brew upgrade is as simple as pinning it via brew pin <formula>. To un-pin it, simply invoke brew unpin <formula>.
It is worth noting that brew upgrade <formula> will still update the formula regardless of whether or not it is pinned.
Caveat: This answer is no longer valid for recent versions of Homebrew, since brew pin has been removed.